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The expression [tex]$7x^2 + 9x^6 - 8x^6$[/tex] is equivalent to [tex]$bx^2$[/tex], where [tex]$b$[/tex] is a constant. What is the value of [tex]$b$[/tex]?

Answer :

To simplify the expression [tex]7x^2 + 9x^6 - 8x^6[/tex], we should first combine like terms.

  1. Identify like terms in the expression:

    • The terms [tex]9x^6[/tex] and [tex]-8x^6[/tex] are like terms because they both involve [tex]x^6[/tex].
    • The term [tex]7x^2[/tex] is separate, as it involves [tex]x^2[/tex].

  2. Combine the like terms [tex]9x^6[/tex] and [tex]-8x^6[/tex]:
    [tex]9x^6 - 8x^6 = 1x^6 = x^6[/tex]

  3. Substitute [tex]x^6[/tex] back into the original expression:
    [tex]7x^2 + x^6[/tex]

However, the problem statement asks for the expression to be equivalent to [tex]bx^2[/tex], indicating we only focus on the [tex]x^2[/tex] term. Since there's no additional [tex]x^2[/tex] term to combine, we realize that we should disregard the [tex]x^6[/tex] term, as it doesn't contribute to the [tex]x^2[/tex] part we need.

Therefore, the expression simplifies directly from its original form to just the [tex]x^2[/tex] term:
[tex]7x^2[/tex]

Thus, the value of [tex]b[/tex], which is the constant in front of [tex]x^2[/tex], is [tex]7[/tex]. Hence, [tex]b = 7[/tex].

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